Question

1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 1: a-d

Answer 1

Given the indicial expressions, we can find their solution below.

Step-by-step explanation

Part A: Divison

`(x^9)/(x^7)`

If the two terms have the same base (in this case x) and are to be divided their indices are subtracted.

`\begin{gathered} In\text{ }general:(x^m)/(x^n)=x^(m-n) \\ Hence,(x^9)/(x^7)=x^(9-7)=x^2 \end{gathered}`

Answer:

`x^2`

Part b: Brackets

`(x^7)^9`

If a term with a power is itself raised to a power then the powers are multiplied together.

`\begin{gathered} In\text{ }general:(x^m)^n=x^(m* n) \\ Hence(x^7)^9=x^(7*9)=x^(63) \end{gathered}`

Answer:

`x^(63)`

Part C: Negative powers

`(x)^(-9)`

A negative power can be written as a fraction.

`\begin{gathered} In\text{ }general:x^(-m)=(1)/(x^m) \\ Hence,\text{ x}^(-9)=(1)/(x^9) \end{gathered}`

Answer:

`(1)/(x^9)`

Part D: Multiplication

`x^7* x^9`

If the two terms have the same base (in this case x) and are to be multiplied together their indices are added.

`In\text{ }general:x^m* x^n=x^(m+n)`

Answer:

`x^7* x^9=x^(7+9)=x^(16)`

Answer:

`x^(16)`